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RUN REVIEW · Specialist Mathematics · Units 1 & 2 · Tech-free

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11 Sep 2026, 9:17 p.m.

20Serious score
01 A student is checking a worked solution. The vector from A to B is
A \(\vec b-\vec a\) Endpoint position minus start position.
B \(\vec a\cdot\vec b\) This does not satisfy the stated relationship.
C \(\vec a-\vec b\) This does not satisfy the stated relationship.
D \(\vec a+\vec b\) This does not satisfy the stated relationship.

Written for icaijy.com · U1–2 · Vectors · answered at 100 ms

02 A student is checking a worked solution. A geometric sequence with ratio r has \(u_n=\)
A \(nr\) This does not satisfy the stated relationship.
B \(u_1r^n\) This does not satisfy the stated relationship.
C \(u_1+(n-1)r\) This does not satisfy the stated relationship.
D \(u_1r^{n-1}\) There are n−1 ratio multiplications from the first term.

Written for icaijy.com · U1–2 · Sequences · answered at 100 ms

03 During a one-minute revision round: \(i^2=\)
A −1 This defines the imaginary unit.
B i This does not satisfy the stated relationship.
C 0 This does not satisfy the stated relationship.
D 1 This does not satisfy the stated relationship.

Written for icaijy.com · U1–2 · Complex numbers · answered at 100 ms

04 During a one-minute revision round: The vector from A to B is
A \(\vec a\cdot\vec b\) This does not satisfy the stated relationship.
B \(\vec a+\vec b\) This does not satisfy the stated relationship.
C \(\vec a-\vec b\) This does not satisfy the stated relationship.
D \(\vec b-\vec a\) Endpoint position minus start position.

Written for icaijy.com · U1–2 · Vectors · answered at 100 ms

05 The sum of degrees in an undirected graph equals
A the number of vertices This does not satisfy the stated relationship.
B twice the number of vertices This does not satisfy the stated relationship.
C twice the number of edges Each edge contributes two degree incidences.
D the number of edges This does not satisfy the stated relationship.

Written for icaijy.com · U1–2 · Graph theory · answered at 100 ms

06 A student is checking a worked solution. The determinant of \(\begin{pmatrix}a&b\\c&d\end{pmatrix}\) is
A \(ac-bd\) This does not satisfy the stated relationship.
B \(ab-cd\) This does not satisfy the stated relationship.
C \(a+d\) This does not satisfy the stated relationship.
D \(ad-bc\) Use ad−bc.

Written for icaijy.com · U1–2 · Matrices · answered at 100 ms

07 Which response best completes this VCE-style item? A square matrix is invertible exactly when its determinant is
A negative only This does not satisfy the stated relationship.
B zero This does not satisfy the stated relationship.
C non-zero A zero determinant means singular.
D one only This does not satisfy the stated relationship.

Written for icaijy.com · U1–2 · Matrices · answered at 100 ms

08 During a one-minute revision round: The conjugate of \(3-2i\) is
A \(3-2i\) This does not satisfy the stated relationship.
B \(2+3i\) This does not satisfy the stated relationship.
C \(3+2i\) Change the sign of the imaginary part.
D \(-3+2i\) This does not satisfy the stated relationship.

Written for icaijy.com · U1–2 · Complex numbers · answered at 100 ms

09 During a one-minute revision round: If \(a\mid b\) and \(a\mid c\), then
A \(bc\mid a\) This does not satisfy the stated relationship.
B \(a\mid(b+c)\) Divisibility is preserved under integer linear combinations.
C \(b\mid a\) This does not satisfy the stated relationship.
D \(a=b+c\) This does not satisfy the stated relationship.

Written for icaijy.com · U1–2 · Number · answered at 100 ms

10 During a one-minute revision round: A geometric sequence with ratio r has \(u_n=\)
A \(u_1r^n\) This does not satisfy the stated relationship.
B \(u_1r^{n-1}\) There are n−1 ratio multiplications from the first term.
C \(u_1+(n-1)r\) This does not satisfy the stated relationship.
D \(nr\) This does not satisfy the stated relationship.

Written for icaijy.com · U1–2 · Sequences · answered at 100 ms

11 \(i^2=\)
A 0 This does not satisfy the stated relationship.
B 1 This does not satisfy the stated relationship.
C −1 This defines the imaginary unit.
D i This does not satisfy the stated relationship.

Written for icaijy.com · U1–2 · Complex numbers · answered at 100 ms

12 Which response best completes this VCE-style item? The modulus of \(3+4i\) is
A 5 Use the Pythagorean theorem.
B 1 This does not satisfy the stated relationship.
C 7 This does not satisfy the stated relationship.
D 25 This does not satisfy the stated relationship.

Written for icaijy.com · U1–2 · Complex plane · answered at 100 ms

13 Which response best completes this VCE-style item? \(\cos(A-B)=\)
A \(\cos A\cos B-\sin A\sin B\) This does not satisfy the stated relationship.
B \(\sin A\cos B\) This does not satisfy the stated relationship.
C \(\cos A\cos B+\sin A\sin B\) Use the cosine difference identity.
D \(\cos A-\cos B\) This does not satisfy the stated relationship.

Written for icaijy.com · U1–2 · Trigonometry · answered at 100 ms

14 The determinant of \(\begin{pmatrix}a&b\\c&d\end{pmatrix}\) is
A \(ac-bd\) This does not satisfy the stated relationship.
B \(a+d\) This does not satisfy the stated relationship.
C \(ab-cd\) This does not satisfy the stated relationship.
D \(ad-bc\) Use ad−bc.

Written for icaijy.com · U1–2 · Matrices · answered at 100 ms

15 During a one-minute revision round: The negation of “all integers are positive” is
A no integers exist This does not satisfy the stated relationship.
B at least one integer is positive This does not satisfy the stated relationship.
C all integers are not positive This does not satisfy the stated relationship.
D at least one integer is not positive Negating a universal statement produces an existential counterexample.

Written for icaijy.com · U1–2 · Logic · answered at 100 ms

16 Which response best completes this VCE-style item? The conjugate of \(3-2i\) is
A \(3-2i\) This does not satisfy the stated relationship.
B \(2+3i\) This does not satisfy the stated relationship.
C \(3+2i\) Change the sign of the imaginary part.
D \(-3+2i\) This does not satisfy the stated relationship.

Written for icaijy.com · U1–2 · Complex numbers · answered at 100 ms

17 During a one-minute revision round: \(\cos(A-B)=\)
A \(\cos A\cos B-\sin A\sin B\) This does not satisfy the stated relationship.
B \(\cos A\cos B+\sin A\sin B\) Use the cosine difference identity.
C \(\sin A\cos B\) This does not satisfy the stated relationship.
D \(\cos A-\cos B\) This does not satisfy the stated relationship.

Written for icaijy.com · U1–2 · Trigonometry · answered at 100 ms

18 Which response best completes this VCE-style item? The scalar projection of a onto non-zero b is
A \(\vec a\times\vec b\) This does not satisfy the stated relationship.
B \(\frac{|\vec b|}{|\vec a|}\) This does not satisfy the stated relationship.
C \(|\vec a||\vec b|\) This does not satisfy the stated relationship.
D \(\frac{\vec a\cdot\vec b}{|\vec b|}\) Divide the dot product by the magnitude of b.

Written for icaijy.com · U1–2 · Geometry · answered at 100 ms

19 A geometric sequence with ratio r has \(u_n=\)
A \(u_1r^n\) This does not satisfy the stated relationship.
B \(nr\) This does not satisfy the stated relationship.
C \(u_1r^{n-1}\) There are n−1 ratio multiplications from the first term.
D \(u_1+(n-1)r\) This does not satisfy the stated relationship.

Written for icaijy.com · U1–2 · Sequences · answered at 100 ms

20 During a one-minute revision round: The scalar projection of a onto non-zero b is
A \(\vec a\times\vec b\) This does not satisfy the stated relationship.
B \(|\vec a||\vec b|\) This does not satisfy the stated relationship.
C \(\frac{|\vec b|}{|\vec a|}\) This does not satisfy the stated relationship.
D \(\frac{\vec a\cdot\vec b}{|\vec b|}\) Divide the dot product by the magnitude of b.

Written for icaijy.com · U1–2 · Geometry · answered at 100 ms

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